This seems utterly silly. It's like saying "I don't believe we should use the internet it's against my religion" and then trying to work a tech job without it.
Maybe I can go to work in a tech company and object to computers. I only use a typewriter. I also rode a horse to get here.
This only seems like it could backfire on the individual. Everyone else in the company is going to use it and come midyear review, they will have run laps around you and your pile of sticky notes and spreadsheets, using your inbox like a filing system.
My religion does not permit me to use Agile. I only track my work on a notepad I keep in my drawer. I won't go to the daily stand, won't participate in sprint planning nor PI planning. Hey, why is everyone getting more done than I am?